Minnesota has Favre, Peterson, great defense, and a perfect record, but the Steelers are favored for several reasons.

PITTSBURGH – Adrian Peterson, the best running back in the world, is coming to town with Brett Favre, arguably the greatest quarterback ever, with a defense that’s stopped the run better than anyone else in the NFL each of the last three seasons.

Add it up and it’s easy to understand why the Minnesota Vikings are 6-0, and also why the 4-2 Steelers are so excited about the 1 p.m. game at Heinz Field.

“We’re underdogs at home, so it’s fun,” said Steelers quarterback Ben Roethlisberger. Only thing: The team that doesn’t have the superstar running back, the iconic quarterback, and the impenetrable run defense, is favored.

The Steelers are favored by four points over the Vikings, and, really, no one’s wondering why, because:

* The Steelers have a pretty solid run defense themselves.

The Vikings may have been the spoiler in the Steelers’ attempt to lead all defensive categories last season, but the Steelers rank right with them as elite run defenders.

Since Dick LeBeau returned to coordinate the defense in 2004, the Steelers have ranked among the top three run-stopping units in the league each season. And they’ve only allowed four 100-yard rushers in the 96 LeBeau-coordinated games (including 10 playoff games).

Of course, left defensive end Aaron Smith is out for the year. In the first game he missed last Sunday, the Cleveland Browns rarely tested replacement Travis Kirschke. The Browns ran right only 8 times for 16 yards. They had better luck running left 10 times for 71 yards.

“Well, the better offensive linemen were over there,” said Steelers nose tackle Casey Hampton. “You’re going to run to where your money’s at.”

In the Vikings’ case, “the money” is on the same left side of the offensive line with tackle Bryant McKinnie and guard Steve Hutchinson. Does Hampton expect Peterson to follow the money as well?

“This guy, he can go anywhere,” Hampton said. “They seem to favor that side, but he cuts it back all the time and you never know where he’s going to hit it.”

Last week, Peterson pushed his NFL-leading rushing total to 618 yards (5.2 avg.) by rushing for 143 against the Baltimore Ravens.

Favre, at 40, remains a championship-caliber quarterback. He’s making so few mistakes that his 109.7 passer rating is well above his career high of 99.5 back in 1995.

But Ben Roethlisberger is in his physical prime and is playing the best football of his career. He’s completing 72.5 percent of his passes and leading the league with a 9.12 yards-per-attempt average. Those numbers received a boost with the emergence of Rashard Mendenhall in the backfield.

The Steelers’ first-round draft pick in 2008, Mendenhall stepped in for an injured Willie Parker and rushed for 304 yards (5.0 avg.) in three games to steal the job. He mixes with the Steelers’ pass-game weapons to provide balance to an offense that’s averaging 461 yards per game with him as the primary runner and 346 without him.

Of course, the Vikings’ front wall, led by pass-rushing RDE Jared Allen and “man-child” RDT Kevin Williams, will be Mendenhall’s stiffest challenge.

“This is a barometer,” said Steelers right guard Trai Essex. “Minnesota has been one of the best D-lines in the NFL for some time now. It’s a barometer for where we are as an O-line to see how we do against one of the better lines in the league.”

* The Vikings have their holes, too.

While the Steelers have lost Smith, and Troy Polamalu is still bothered by an injured knee, the Vikings have their own problems. The lesser is the mediocre play of the right side of their offensive line. Rookie right tackle Phil Loadholt is a massive 6-8, 343 pounds who’s struggled with his agility thus far and will be up against hungry pass-rusher LaMarr Woodley.

The Vikings’ bigger problem, though, is the loss of Pro Bowl cornerback Antoine Winfield. His replacement, Karl Paymah, was targeted last week by the Ravens in a fourth-quarter rally that netted 21 points in eight minutes. The Vikings will use either Paymah, rookie Asher Allen, or nickel back Benny Sapp as their primary replacement for Winfield, who, according to Steelers offensive coordinator Bruce Arians, is “a great tackler, a very solid cover guy. They’ll be short in nickel because they’ll be down to their fourth guy.

“He’s such a good player. Them missing him is like us missing Troy.”

* The Steelers have the intangibles in their favor.

While the Vikings enter the game with a 2.5-game lead in their division over a team they’ve already defeated, the Steelers are in a tight three-team race that will probably go down to the wire, so this game is more important to them.

They’re also playing at home against an undefeated team. The last time a 6-0 team came into Heinz Field, the Steelers whipped the New England Patriots, 34-20, back in 2004. And the following week, the Steelers hammered the 7-0 Philadelphia Eagles, 27-3.

The Vikings also employ a West Coast offense, an offense that LeBeau has contained well as a coordinator. Last season’s 15-6 loss to the Eagles was the first loss to such an offense for LeBeau since he returned to the Steelers. That stretch included a 20-10 win over Favre at Green Bay in 2005.

LeBeau was asked if that’s part of the reason he’s excited about today’s game.

“Well,” he said, “I think the fact that we’re playing an undefeated football team, a team with a great running back, and maybe the greatest quarterback, that should be pretty good motivation for us.”